Regarding the Gaussian Mixture Model(GMM) for classification and clustering. the weight for each Gaussian component are arbitrarily set as an average of total numbers of components.
This is conducted as a common sense in most textbooks, papers and practical uses.
Any clues are welcome
One sensible thing to do is to set the mixture weight to the prior probabilities, but in most cases I have seen mixture weight is a hidden variable and estimated through EM.
You could do a k-means clustering with k equal to the number of mixtures you want and initialize the weights proportionately. This is another way to go about it and it somewhat makes sense.
If you do know the mixture membership for some of your training data, you could use that and estimate the prior probability and use it to initialize your mixture weights, but I have never seen a case like that.
On a side note, there is no principled method to set the number of mixtures and I think the scientific community is pretty convinced there is none.
